1. Field of the Invention
This invention is related in general to devices that perform linear transformations, such as Fourier and wavelet transforms. In particular, the invention relates to a programmable analog circuit capable of performing any discrete linear transformation and its inverse.
2. Description of the Related Art
Linear transforms are very useful tools in science and technology. For example, Fourier transforms and inverse transforms are commonly utilized in many fields to analyze, design and implement signal processing, such as for defense and aerospace applications (radar, sonar, synthetic aperture radar, electronic warfare), medical diagnostic imaging (ultrasound, computed tomography, magnetic resonance imaging), telecommunications (broadband, wireless, digital video broadcasting), instrumentation and measurement (spectrum analysis, radio astronomy), and industrial vision (non-destructive testing, pattern recognition).
In all such applications, Fourier transforms are implemented with digital computers that utilize well known Discrete Fourier Transform (DFT) algorithms. For example, using current state-of-the-art processors, the algorithm known as the Fast Fourier Transform (FFT) can produce a 1024-point transform in approximately 10 μs, with a corresponding maximum data throughput of about 100 kHz. Multiple, staggered processors may be used operating in parallel in order to increase speed, but with increased power requirements that can exceed the capability of conventional bus configurations. Accordingly, the current implementation of DFT algorithms in digital computers is limited by hardware constraints.
Progress has been made in an effort to increase the processing speed of FFT algorithms by reducing the number of computations. For example, U.S. Pat. No. 5,987,005 describes an approach whereby DFT and inverse DFT operations are computed using the same computing device, thereby optimizing computational efficiency. The very high number of binary operations required to implement these algorithms and the increased power requirements associated with faster implementations remain a severe limiting factor in efforts to provide significant improvements in the speed of transform and inverse transform computation.
Therefore, there is still a need for a faster approach to the computation of linear transforms that does not also require unacceptably high power consumption. This invention has achieved this objective by effecting the transform and inverse-transform computations using analog devices.